# Theta Proxy RM

Thetaris introduces Theta Proxy, a technology which allows multiple evaluations of a pricing function with vastly accelerated processing time compared to traditional repeated evaluation. This technological breakthrough presents a significant step forward for the application of Monte Carlo pricing in time sensitive applications such as risk management.

Monte Carlo methods are known for their wide applicability to pricing problems, this flexibility extending to even the most exotic derivative. However, this advantage has not yet been successfully exploited due to tight performance constraints in bank wide risk measurements.

Now, for the first time, the Theta Proxy presents a Monte-Carlo based evaluation strategy for pricing financial products under a huge number of input factor scenarios. Any complex financial product can now be priced at a speed and an accuracy previously only achievable in a single product evaluation. Now these prices can be processed and retrieved all at once.

## Usage Scenario

Institution wide risk management applications require a large number of derivatives to be priced in the context of potential future scenarios. The Basel II directive allows for a significant reduction in capital requirements when the potential future exposure is measured accurately. To match current guide lines each product in the portfolio must be priced in multiple scenarios. A typical example would require 5000 scenarios of potential future market parameters sampled at 250 individual time steps. Given a daily evaluation, this means 1.25 mn prices have to be computed, leaving only fractions of a second for each individual evaluation. Without the Theta Proxy there is simply no possibility to price complex products using Monte Carlo simulation at the frequency required. For a financial institution this means risk figures have to be over estimated, leading to unnecessarily large capital reserves.

## Technology

Theta Proxy is a new technology for accelerated Monte Carlo evaluation. It is applicable whenever a range of similar evaluations are performed with near by, but different start parameters. In typical risk management settings a scenario engine generates potential future market parameters according to physically observed statistics. Straight forward Monte Carlo leads to a range of simulations. No results are reused.

Straight forward Monte Carlo pricing on physical scenarios without reusing results from similar simulations.

The new technology facilitates an incremental Monte Carlo simulation approach. Packaged as Theta Proxy, the technology is available as an add-on module to the Theta Suite. One of Theta Suite's unique features is the analysis of compact product definitions in ThetaML and extraction of fast yet precise algorithms for pricing routines. The Theta Proxy makes further use of the product structure and the structure of incoming physical pricing scenarios. The method utilizes the fact that functions are smooth in most regions and that exercise boundaries are equal within each time step. The method can be used to increase speed and accuracy of product pricing.

Optimized scenario placement using the Theta Proxy technology